Turn over the rug and lay it on the carpet.
How to get rugs to lay flat on carpet.
Turn over the rug with the right side down.
Lay a damp towel over the edges and iron them flat.
Many times this will allow the rug to lay smooth for a while.
Cut tape to fit each edge of the rug.
Apply carpet tape around the edges of the rug.
This should flatten the areas out.
Apply the tape to the edges of rug.
With the towel still covering the carpeted area hold down the iron and press.
Double sided tape could be used in place of the carpet tape.
So the bottom line is that yes you can put an area rug over wall to wall carpet.
Then take an iron and set it to a medium heat.